Comments on contact terms and conformal manifolds in the AdS/CFT correspondence

• Published in: Progress of theoretical and experimental physics Vol. 2021; no. 1
• Main Authors: Sakai, Tadakatsu, Zenkai, Masashi
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.01.2021
• Subjects: B21; B32
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptaa164

Abstract We study the contact terms that appear in the correlation functions of exactly marginal operators using the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. It is known that CFT with an exactly marginal deformation requires the existence of the contact terms with their coefficients having a geometrical interpretation in the context of conformal manifolds. We show that the AdS/CFT correspondence captures properly the mathematical structure of the correlation functions that is expected from the CFT analysis. For this purpose, we employ a holographic renormalization group to formulate a most general setup in the bulk for describing an exactly marginal deformation. The resultant bulk equations of motion are nonlinear and solved perturbatively to obtain the on-shell action. We compute three- and four-point functions of the exactly marginal operators using the GKP–Witten prescription, and show that they match the expected results precisely. The cut-off surface prescription in the bulk serves as a regularization scheme for conformal perturbation theory in the boundary CFT. As an application, we examine a double OPE limit of the four-point functions. The anomalous dimensions of double trace operators are written in terms of the geometrical data of a conformal manifold.